Molality Calculator

Molality (mol/kg) = moles of solute ÷ kilograms of solvent · Mass percent = solute ÷ (solute + solvent) × 100

molality

Moles of solute per kilogram of solvent. Written mol/kg, and usually given the symbol b or m

mass of solute

What you weighed out and dissolved, in grams or milligrams

mass of solvent

The mass of the liquid doing the dissolving — the water, weighed on its own, before the solute goes in. Not the mass of the finished solution

mass percent

The solute's share of the total mass, as a percentage. It uses masses on both sides of the division, never moles

Use molality when the temperature moves — boiling point elevation, freezing point depression and anything else tied to colligative properties is written in mol/kg precisely because the number must not shift when the solution is heated. It is also the right unit when the two components are weighed rather than measured out, since a balance gives mass directly. For a solution made up in a volumetric flask and used at room temperature, molarity is the more convenient of the two, and it is what almost every reagent label means by M.

1. One mole of salt in one kilogram of water

   1. Moles of solute: 58.44 ÷ 58.44 = 1 mole of sodium chloride
   2. Solvent in kilograms: 1000 grams of water = 1 kilogram
   3. Divide: 1 ÷ 1 = 1 mol/kg
   4. Mass percent: 58.44 ÷ (58.44 + 1000) × 100 = 5.521%

   Note where the 5.521% comes from: the denominator is the total mass, solute plus solvent. Dividing by the solvent alone would give 5.844%, and dividing the moles by the total mass would be a third answer again. Three readings of "per cent" that differ in the first decimal place, which is why the units are spelled out on this page.

2. The same mole in half the water

   1. Moles of solute are unchanged: 1 mole
   2. Solvent in kilograms: 500 grams = 0.5 kilograms
   3. Divide: 1 ÷ 0.5 = 2 mol/kg
   4. Mass percent: 58.44 ÷ (58.44 + 500) × 100 = 10.465%

   Halving the solvent doubles the molality and roughly doubles the mass percent, but the two do not double together exactly — 5.521% becomes 10.465% rather than 11.042%, because the total mass in the denominator shrank as well. Mass percent and molality are different functions of the same two masses and only ever coincide by accident.

The denominator here is the mass of the solvent, not the mass of the finished solution and not its volume, and that is the single thing most likely to be misread. This page therefore asks for the two masses separately, and it cannot help you if what you actually know is the volume of the solution. Converting a molality to a molarity is not a multiplication: it needs the density of the finished solution, and that density depends on the concentration you are trying to find, so the conversion is a lookup rather than an arithmetic step. The reason molality is worth the trouble is that it does not move with temperature — a solution's volume grows when it is warmed, so its molarity falls, while the masses on both sides of this division stay put. Mass percent here is a ratio of masses and has nothing to do with mole fraction, which appears when you compare numbers of particles rather than amounts of matter; a 5.5% solution by mass is nowhere near 5.5% of its molecules, because water molecules are much lighter than salt formula units. Small amounts are reported to five decimal places, so a milligram of salt in a kilogram of water comes out as 0.00002 mol/kg rather than as zero, which is the honest answer at that scale but is also at the edge of what the display can show. Finally, this page assumes the solute dissolves completely and does not react with the solvent; it says nothing about whether the solution is saturated.

What is molality, and how do you calculate it?

Moles of solute per kilogram of solvent, written mol/kg and usually given the symbol b. One mole of salt dissolved in one kilogram of water is a 1 mol/kg solution, and the same mole in half a kilogram of water is 2 mol/kg. The denominator is the weight of the liquid doing the dissolving, weighed on its own — not the weight of the finished solution, and not its volume. That choice of denominator is what makes molality independent of temperature.

What is the difference between molality and molarity?

The denominator. Molarity is moles per litre of solution; molality is moles per kilogram of solvent. A litre is a volume, so it expands when the solution is warmed and the molarity falls; a kilogram is a mass, so it does not. The two numbers are also different in size even at room temperature, because a litre of solution weighs more than a kilogram: a 1 mol/kg salt solution is roughly 0.98 M, the gap coming from the water the salt displaced. Use molarity for making up solutions at the bench, and molality for anything whose temperature will change.

Can I convert molality to molarity?

Not from these two numbers alone — you also need the density of the finished solution. Molarity is moles per litre, and getting from a mass of solvent to a volume of solution means knowing how much the whole thing weighs per millilitre. Since the density itself depends on how concentrated the solution is, the conversion is a lookup in a table rather than a formula you can apply blind. If you have the density, the step is: total mass = solute + solvent, volume = total mass ÷ density, molarity = moles ÷ volume in litres.

Is mass percent the same as molality?

No — they use different units on both sides of the division. Molality is moles divided by kilograms of solvent; mass percent is grams of solute divided by grams of the whole mixture, times a hundred. A 1 mol/kg salt solution is 5.521% by mass, and the two figures would only ever match by coincidence. Which one you want depends on the question: mass percent for a composition, molality for anything that depends on how many particles are present rather than how much they weigh.

Why does a tiny amount show as 0.00002 instead of zero?

Because a milligram of salt in a kilogram of water really is 1.7 × 10⁻⁵ mol/kg, and the molality line carries five decimal places, so the smallest amount the mass fields accept still lands on a non-zero figure rather than collapsing to 0.00000. That matters because a zero in a result panel reads as "nothing dissolved" rather than "a very little". The scale runs the other way too: a tonne of solute in a tonne of solvent is 17111.56742 moles and 17.1 mol/kg, since the denominator there is a thousand kilograms.

• SI Units — Amount of Substance: the mole and the mole per cubic metre — National Institute of Standards and Technology (NIST)
• Standard Atomic Weights — abridged to four significant figures — Commission on Isotopic Abundances and Atomic Weights (CIAAW), IUPAC